Significance

Electrides are ionic materials in which electrons act as anions. Solvated electrons in ammonia are one of the early known examples of such anions in liquids. Electron anions in crystalline materials have previously been shown to dramatically alter their electronic properties, for example, to turn an insulator into a superconductor with minimal changes in the structure and stoichiometry. We show that electron anions modify the disordered glass network by creating highly mobile weak links, thus fundamentally altering the thermodynamic and electronic properties of the network and enabling a new design paradigm for amorphous materials.

Abstract

Properties of glasses are typically controlled by judicious selection of the glass-forming and glass-modifying constituents. Through an experimental and computational study of the crystalline, molten, and amorphous [Ca12Al14O32]2+ ⋅ (e–)2, we demonstrate that electron anions in this system behave as glass modifiers that strongly affect solidification dynamics, the glass transition temperature, and spectroscopic properties of the resultant amorphous material. The concentration of such electron anions is a consequential control parameter: It invokes materials evolution pathways and properties not available in conventional glasses, which opens a unique avenue in rational materials design.

One of the key challenges in materials design is identification of degrees of freedom that ensure robust control of the properties of interest. Small changes in composition of crystalline materials can lead to large changes in their electronic properties, such as optical absorption and electrical conductivity (1). Similarly, a small concentration of (co)dopants in amorphous materials can be used to control their optical properties (2, 3). Glass properties are typically controlled by varying composition or processing conditions (4). However, delicate control of viscosity and glass transition temperature in multicomponent materials (Tg) has remained elusive due to the collective origin of these properties. Substitution of atomic anions with electron anions in materials to form electrides (5, 6) introduces an additional degree of freedom. Here we demonstrate that electron anions dramatically change dynamics of atoms in an inorganic amorphous material, which strongly affects its Tg. Extending the concept of electron anions to other amorphous materials would provide a powerful instrument for the design of glasses with finely tuned characteristics.

Calcium aluminates (CA), composed of CaO and Al2O3, represent a common family of oxide glasses. Whereas pure Al2O3 is a poor glass former, blending it with CaO leads to the formation of stable glasses composed of AlO4 tetrahedra with strong and directional covalent bonds instead of nondirectional ionic bonds in bulk Al2O3 (7). In contrast, Ca-O bonds retain their ionic character; they are weaker than Al-O bonds and lack a preferred orientation, which enables motion of the AlO4 tetrahedra relative to each other. Hence, the Tg of stoichiometric CA systems decreases by ∼50 K as the CaO content increases from 57 mol% to 70 mol% (Fig. 1). This relatively narrow interval of Tg variation with composition is typical of multicomponent glasses (8, 9). The Tg for stoichiometric [Ca12Al14O32]2+ ⋅ (O2–) (C12A7:O2–) is in line with the general trend for CA systems (∼830 °C). Conceptually, Tg of a glass network can be further modified by introducing weak links. For example, Tg of CA systems can be modified by addition of CaF2, which reduces the number of Al-O-Al bridges between the tetrahedral structural elements and decreases their viscosity. As a result, Tg decreases by ∼75 K at a mole fraction of 20% CaF2 (10). Similar effects can also be achieved by replacing lattice oxygens with other anions such as H− and OH− (11). Processing C12A7 in a reducing environment leads to replacement of clathrated oxygens with electrons (12, 13), forming [Ca12Al14O32]2+ ⋅ (O2–)1–x(e–)2x, referred to as C12A7 electride (C12A7:e–) due to electrons functioning as anions (5, 14, 15). In crystalline C12A7:e–, the electrons occupy the cage conduction band (CCB) states associated with the lattice cages (16, 17), leading to polaron-type conduction at x < ∼0.5 and metallic conduction at x > 0.5 (13, 16). The exceptionally low work function of crystalline C12A7:e– (2.4 eV) (18) is used in electron field emitters (19, 20), field-effect transistors (21), resistive memory (22), and enhancement of catalytic activity for ammonia synthesis (23). Amorphous C12A7:e– (a-C12A7:e–) also has a low work function (24), providing a host of new applications and technologies at the industrial scale. Whereas the structure and electronic properties of the crystalline C12A7 have been extensively investigated, there is a handful of experimental and computational studies of a-C12A7:O2– (25, 26) and a-C12A7:e– (27, 28), focused on the structural properties of a-C12A7. However, the effects of nonstoichiometry have remained elusive.

Glass transition temperature (Tg) in CaO-Al2O3 glasses as a function of CaO content and electron anion concentrations. Inset shows Tg values of a-C12A7:e– for several electron concentrations determined by differential thermal analysis. Data of conventional glasses in this system (blue) are taken from the literature (Table S1).

Electron anions, even at low concentrations (Ne), lead to dramatic changes in the Tg values (Fig. 1): for x = 0.095 (Ne = 2.2 × 1020 cm–3) the Tg drops by 50 °C to ∼770 °C and for x = 0.475 (Ne = 1.1 × 1021 cm–3) it decreases by over 40 °C more, to ∼725 °C, for a total change of over 90 °C. These data support a recent report where only one Tg value for an electron-rich C12A7 was reported (29). The change in Tg in this CaO-Al2O3 system induced per mole of electron anions is a factor of 6 greater than that induced per mole of F−. Such a dramatic Tg effect is remarkable and, if understood and controlled, promises the development of a fundamental class of multicomponent amorphous materials in which Tg is responsive to small compositional changes.

The experimental results raise two questions: (i) Why does the effect of oxygen deficiency outweigh the effect of CaO/Al2O3 ratio? And (ii) can it be realized and harnessed in other systems? Here we reveal atomic-scale mechanisms of how electron anions in C12A7 alter the lattice dynamics in the crystalline and molten phases, ultimately affecting the Tg, structure, and electronic properties of this material. To reveal the distinctive role of the electron anions in the glass formation process and the resulting properties, we conducted ab initio (density functional theory) spin-polarized molecular dynamics (AIMD) simulations, in which crystalline [Ca24Al28O64]4+ ⋅ (O2–)2(1–x)(e–)4x (for x = 0 and x = 1) was subjected to heat–compress–quench treatments mimicking the experimental procedure. Analysis of the electronic properties and structure evolution with T and Ne reveals characteristic structural and spectroscopic signatures associated with the electron anions and allows us to (i) explain the strong dependence of the Tg on Ne and (ii) propose the formation mechanism that may hold for other materials containing electron anions.

Methods

Experimental Details.

Stoichiometric C12A7 can be readily converted to a glass form by a conventional melt-and-quench method. Whereas the chemical composition of C12A7 electride (C12A7:e–) differs from that of stoichiometric C12A7 by only 3% of the oxygen content, C12A7:e– glass could not be obtained by the same method due to very fast crystallization of the melt. To overcome this problem, we designed a process that ensures C12A7:e– cooling at a shorter timescale than crystallization. This result was achieved with the help of the twin-roller apparatus shown in Fig. S1 and described in detail elsewhere (29). The sintered powder of the polycrystalline C12A7:e– was melted in the controlled O2 atmosphere with the gas pressure (pO2) of ∼10−23 atm, using a floating zone furnace with lamp heaters. The melt was dropped into the space between the rotating twin rollers. The low pO2 (10–23 atm) atmosphere was kept around the twin roller apparatus to prevent the oxidation of melt and the formation of glass flakes. The amorphous nature of the resulting samples was confirmed by X-ray diffraction experiments and by electron diffraction experiments carried out for a selected part of the material in the transmission electron microscopy mode. The electron concentrations and the chemical compositions of the resulting glasses were determined by iodometric titration and X-ray fluorescence, respectively. The Ca:Al atomic ratio in the samples was 47 ± 1:53 ± 1, which is almost the same as the Ca:Al ratio in crystalline C12A7. The glass-transition temperature (Tg) was determined by differential thermal analysis (DTA). Before conducting the DTA measurements, the sealed glass was annealed at ∼650 °C (heating rate was 20 K/min) in the ambient atmosphere to alleviate quenching-induced stress. The resulting glass flakes were sealed into a thin wall SiO2 glass tube to suppress the oxidation during heating.

Apparatus used for fabrication of C12A7:e– glass. Infrared lamp heating furnace for the floating zone is connected to the twin rollers. The atmosphere in the furnace was kept at pO2 ∼ 10−23 atm, using a hollow SiC rod; pO2 in the vicinity of the twin roller was kept at ∼10−16 atm to prevent oxidization of the melt and the formation of glass flakes.

Computational Details.

Models of the amorphous stoichiometric (a-C12A7:O2–) and electride (a-C12A7:e–) C12A7 were obtained from the corresponding crystalline forms, using the melt-and-quench approach. The initial crystalline phases were represented using a cubic unit cell [Ca24Al28O64]4+ ⋅ (e–)4 for the electride and [Ca24Al28O64]4+ ⋅ (O2–)2 for the stoichiometric C12A7, respectively, and the lattice constant a0 = 12.0 Å. Their geometrical parameters and electronic properties were in good agreement with the experimental data (16, 30, 31). To separate the effect of the electrons as pseudoanionic species from the effect of the stoichiometry (i.e., the relative content of Al2O3 and CaO components), we conducted simulations on the C12A7 “pseudo-electride,” in which the excess electrons are replaced by a homogeneous electron gas with the density ρ corresponding to the total charge of 4e– per cell: [Ca24Al28O64]4+ ⋅ ρ(4–).

Atomic trajectories were simulated in the microcanonical (constant particle number, volume, and energy) ensemble, using the Vienna Ab Initio Simulation Package (VASP) 5.2.12 (32), the exchange-correlation functional by Perdew–Burke–Ernzerhof (PBE) (33), projector augmented wave (PAW) pseudopotentials (34, 35), and a time step of 0.5 fs. Each molecular dynamics (MD) simulation begins with 4.0 ps of isochoric heating to a target temperature Tmax. After equilibration, the supercell was isotropically compressed in four equal decrements over 16.0 ps until the target density was reached (2.95 g/cm3 and 2.79 g/cm3 for C12A7:e– and C12A7:O2–, respectively). Then, the systems were quenched by uniformly scaling atomic velocities so kinetic energy was decreased by 5.0 eV every 2.0 ps until a temperature of ∼100 K was reached. Finally, the total energies of quenched systems were minimized with respect to the fractional coordinates of all atoms and the cell parameters. Dielectric functions were calculated for selected prerelaxed systems, using VASP 5.4.1 and the HSE06 hybrid functional (36).

Trajectories were visualized using the VMD program (37), and extracted coordinates and band-projected charge densities were visualized using the VESTA program (38). Cyclic structures were identified using R.I.N.G.S 1.2.5 (39), and partial charges were calculated using the Bader method (40). Raman spectra, including resonance effects, were calculated for simplified models of localized electron anions, using NWChem 6.5 (41). Further details of simulation parameters and data analysis are included as Supporting Information.

Results and Discussion

The electronic structure changes in C12A7 after heating and quenching were characterized using the one-electron energies associated with the top of the O 2p valence band (VB) and several lowest states of the CCB. Two representative cases for C12A7:e– (x = 1) are shown in Fig. S2. For the maximum temperature (Tmax) of 1,910 K, the crystalline C12A7:e– did not melt within the simulation time. No significant fluctuations occurred in the energy levels with one notable exception at ∼7 ps into the MD run where the energy of one of the occupied states decreased by over 1 eV due to the formation of a defect center in which two electrons were trapped between two Al species—an Al(2e–)Al center. In contrast, at Tmax = 2,650 K, energies fluctuate until well into the quenching stage of the simulation. Charge distributions and pairwise correlation functions (Figs. S3 and S4) indicate that the system melted and then solidified during this MD run, whereas the four electrons became localized in two defects centers: Al(2e–)Al and Al(2e–)Ca. The solid-to-melt phase transition and quenching are discussed further in Supporting Information.

One-electron energies for heat–compress–quench molecular dynamics trajectories on C12A7:e– for Tmax = 1,910 K (Top) and 2,650 K (Bottom). The initial kinetic energy was added in a single pulse at the first time step. Energies for the spin-up electrons are shown as solid lines and spin-down electrons are shown as dotted lines (Top only); energy differences between spin states were negligible. Excess electrons occupy the states between the VBM and CBM and form bipolarons, Al(2e–)Al and Al(2e–)Ca defect states (Fig. 2 of the main text).

Solid-to-melt transition in C12A7:e–. (A) Radial distribution function gAl–Al(r) after equilibration and lattice compression to the a-C12A7:e– mass density. (B) Negative internal pressure indicates spontaneous lattice compression at elevated temperatures, becoming more favorable above 2,000 K for the electride. (C) Localization of the excess electrons near Al atoms is quantified using the number of Al species with the ionic charge of less than +3.0 |e|. Such charge localization is a rare/transient event at Tmax below 2,310 K and a frequent/persistent event at Tmax of 2,310 K and above, indicating the formation of stable or metastable electron centers.

Quenched structures in C12A7:e–. (A) Radial distribution functions gAl–Al(r) for several C12A7:e– structures at the end of the quenching stage (T ∼ 100 K). Radial distribution functions for systems in which melting occurred are indicated by dotted lines. (B) Dependence of the internal pressure on temperature during isochoric quenching for several values of Tmax.

Similar simulations were conducted for seven values of Tmax. The resulting total energies and mass densities are compared in Fig. 2A. For Tmax > 2,400 K the calculated density of the material was ∼15% higher than that for Tmax < 2,400 K. Although atypical for a glass, which is typically less dense than the corresponding crystalline material (4, 42), it is consistent with the density difference between the amorphous and crystalline C12A7:e– observed experimentally (29), which we attribute to the collapse of the lattice framework and loss of the framework cage space. The topology change is evidenced by the loss of the six-membered Al-O-Al-O-Ca-O rings (Fig. 2A, Inset) connecting the neighboring cages in the crystal and the appearance of other types of six-membered rings; the corresponding changes of the four-membered ring distribution are shown in Fig. S5. The density correlates with the internal energy of the material: More compact structures correspond to larger deviations from the crystalline C12A7:e– and are less thermodynamically stable (Fig. 2A).

Distribution of 4- and 6-membered rings in the nearly crystalline C12A7:e– (Tmax = 1,910 K) and a-C12A7:e– (Tmax = 2,650 K) after quenching. Separation into calcium-rich and aluminum-rich structures in a-C12A7:e– is less distinct than for 6-membered ring structures but is still evident. Ring stoichiometries present in the amorphous material but not in the crystal are indicated by black markers.

The electron anions in quenched C12A7:e– localize in three types of defects; the corresponding one-electron energies relative to the band edges are shown in Fig. 2B and the local structure of electron centers in Fig. 2C. Bipolarons, i.e., pairs of spin-coupled electrons localized in two neighboring distorted cages, closely resemble pairs of electron polarons in crystalline C12A7:e– (16, 27). The spin-up and spin-down electrons have similar charge density distributions and indistinguishable one-electron energies, located within several 10ths of an electronvolt from the conduction band (CB) minimum. The formation of bipolarons is suppressed if the lattice cages deform or collapse. Deformation results in Al(2e–)Ca centers: cage-like structures with two electrons localized between a 3-coordinated Al3+ ion and one or more Ca2+ ions. The corresponding one-electron energies are approximately in the middle of the quenched C12A7:e– band gap. Alternatively, Al(2e–)Al centers (Fig. 2C) are formed either due to the lattice collapse at high Tmax or, at low Tmax, via local deformation of an Al–O–Al angle from ∼140° to ∼70°. The latter mechanism does not necessitate melting of the lattice framework; furthermore, it may provide an opportunity for manipulating glass formation by varying pressure (43). In both cases two Al3+ ions are brought to 2.6–2.8 Å from each other, which creates a deep potential well that traps two electrons. The post-AIMD electronic structure calculations using a hybrid density functional resulted in the same ordering of the defect energy levels and similar electron density distributions. Details of the electronic structure are shown in Fig. S6.

(A) Density of states calculated at the PAW-PBE level of theory for Al(2e–)Ca and Al(2e–)Al centers in amorphous C12A7:e– obtained by quenching from Tmax = 2,650 K and projected on the atomic functions of the constituent Al and Ca atoms. The total density of states (DOS) for the system is overlaid as a black line; the difference is due to the contribution of oxygen ions surrounding the M(2e–)M center. (B) Contributions of the Al and Ca atoms, decomposed over s-type and p-type functions. Most of the metal atom contribution comes from the Al 3s and 3p atomic orbitals, consistent with the σ-type bonding state of the two electrons in both Al(2e–)Ca and Al(2e–)Al centers.

These two-electron defects are fully consistent with the observation that less than 1% of electron anions give rise to unpaired spins, as detected by electron spin resonance spectroscopy (29). Indeed, in Al(2e–)Al and Al(2e–)Ca the spatial distributions of the spin-up and spin-down electrons coincide. In contrast, spin-up and spin-down electrons in bipolarons occupy different regions of space and can become further separated from each other in the process of thermal treatment. Because (bi)polarons are a minority defect (Fig. 2B), the concentration of unpaired spins is low.

According to our statistics, bipolarons are formed if Tmax is below or near the melting temperature (Tm), whereas Al(2e–)Ca centers appear if Tmax is close to Tm or above it. In contrast, the Al(2e–)Al centers form at both low (1,900–2,200 K) and high (>2,550 K) values of Tmax. Their formation at Tmax ∼ Tm appears to be suppressed in favor of bipolarons and Al(2e–)Ca centers. Given that Al(2e–)Al is the most stable defect type, as quantified by one-electron energies, we attribute this effect to the activation of multiple competing kinetic pathways near Tm.

Cross-correlated analysis of the thermodynamic properties of quenched C12A7:e–, atomic trajectories, and electron charge trapping reveals the microscopic origin of the effect of electron anions on Tg. Fig. 3A shows the atomic speed of individual atoms in C12A7:e– and C12A7:O2– averaged over 2-ps intervals, as a function of temperature during the quenching stage. At high temperatures all ions are mobile, with stronger-bonded AlOx units forming near 1,900 K, indicated by the rapid slowing of Al and O species. Glass formation temperature is determined by weaker bonds involving Ca, O, and electron anion species. At 1,100–1,300 K atomic diffusion continues in C12A7:e–, whereas it is negligible in C12A7:O2–. This is consistent with the temperature dependence of the heat capacity (Cv): The electride undergoes a phase transition at ∼1,150 K, whereas the same transition in C12A7:O2– occurs at higher temperatures, peaking near 1,250 K (Fig. 3B). We adopt these temperatures as the Tg values for the C12A7:e– and C12A7:O2–, respectively, and note that (i) these Cv peaks occur at the same temperature as the cessation of Ca and O diffusion and (ii) the difference between them (∼100 K) is very close to the observed difference. The relationship between Tg and electron anions was further tested by replacing them with a homogeneous static charge distribution (ρ−); no corresponding decrease in Tg was observed (Fig. 3B and Fig. S7).

(A) Atomic speed (Å/fs) distributions of individual atoms for C12A7:e– (Top) and C12A7:O2– (Bottom) during quenching. The mobility of Al atoms ceases by T ∼ 1,900 K; Ca and O atoms remain mobile until a substantially lower temperature. (B) Each of these transitions in mobility corresponds to a change in heat capacity, with the lower-temperature transition corresponding to Tg. The presence of electron anions decreases Tg, and no such decrease is observed when they are replaced with a uniform negative charge distribution ρ−. (C) Al ions trapping electron charge (black circles) and the total amount of electron anions trapped near these ions (red triangles). (D) Evolution of selected Al–O and Al–Al distances during the Al(2e–)Al center formation, also manifested in the changes of Qe(Al) in C.

Atomic speed distribution during quenching for the C12A7 pseudoelectride (Tmax = 2,870 K). Because the pseudoelectride does not contain explicitly treated electron anions, the response of this system to thermally induced charge fluctuations takes place on the timescale of atomic motion, i.e., on the same timescale as in the stoichiometric C12A7. Hence, the apparent glass transition temperature of the pseudoelectride (1,300 K) is nearly equivalent to that of the stoichiometric material (1,250 K).

The atomic scale events occurring in quenched C12A7:e– are illustrated in Fig. 3 C and D. Dynamics of the electron anions are illustrated in Fig. 3C (Tmax = 2,650 K), where black circles mark Al atoms that trap electrons and Qe(Al) is the amount of the electron charge summed over all Al species. As the temperature of the system decreases to below 1,500 K, only three Al ions are associated with these electrons. Similarly, variations in Qe(Al) become small at T < 1,200 K, indicating that electron transfer between Al and Ca species as well as between Al and remnants of the lattice cages ceases at this temperature.

Although diffusive motion of Al ceases at ∼1,900 K in both C12A7:e– and C12A7:O2–, Al3+ ions contribute to the lattice dynamics until the system temperature approaches Tg. Fig. 3D shows the interatomic distance between a selected pair of Al3+ ions during the quench stage (Tmax = 2,650 K). At high temperature the distance between these atoms oscillates in the vicinity of 3.5 Å. However, at ∼9 ps into the simulation run (T ∼ 1,500 K), the distance between these atoms rapidly increases to over 4.0 Å and then rapidly decreases to 2.7 Å. This structural rearrangement results in the formation of an Al(2e–)Al center; the signature of this process is also visible in Fig. 3C: The amount of electron charge trapped by Al ions increases sharply at the same time as the Al–Al distance decreases. Furthermore, at ∼12 ps the Al–Al distance increases to ∼4 Å for about 2 ps before decreasing again. This event is accompanied by a simultaneous decrease and then, 2 ps later, an increase of the electron charge trapped by Al species.

Analysis of the AIMD atomic trajectories and charge density distributions reveals that the formation of Al(2e–)Al and Al(2e–)Ca centers is controlled by the correlated motion of the O2– and Al3+ ions, whereby the defect formation step is triggered by thermally driven diffusion of an O2– ion from the first (tetrahedral) coordination shell of an aluminum (Fig. 3D and Fig. S8). As O2– ions diffuse through the melt, the coordination number of Al3+ typically varies between 3 and 5 (Fig. S9). In a-C12A7:O2–, the Al3+ tetrahedral coordination is restored when either another O2– ions diffuses into and occupies the vacant oxygen site or the local structure rearranges from corner-sharing neighboring AlO4 tetrahedra to edge-sharing ones. In contrast, in a-C12A7:e–, electron anions preferentially and rapidly localize at the site of the missing O2– to neutralize the exposed charge and restore the tetrahedral environment, leading to the formation of Al(2e–)Al and Al(2e–)Ca centers. Oxygen ions displaced by electron anions coordinate with adjacent metal atoms to form hypercoordinated species such as 5-coordinated Al3+ (Fig. S9).

Evolution of distances between the aluminum ions involved in the Al(2e–)Al (A) and Al(2e–)Ca (B) centers and their oxygen neighbors during the quench procedure. Shown with different colors are Al-O distances for oxygen that remain in the first coordination shell of Al (black), were diffused out of the first coordination shell (dotted), were diffused into the first coordination shell (gray), were displaced from between the two metal atoms, and were replaced by an electron pair (blue).

(A) Aluminum coordination numbers, i.e., the number of oxygen neighbors per Al, for C12A7:e– quenched from Tmax = 2,650 K. Three aluminum ions were hypo-coordinated at the end of the quench. (B) Coordination numbers for specific aluminum ions involved in the formation of Al(2e–)Al and Al(2e–)Ca centers. Formation of these centers is indicated by the coordination number decreasing to 3 and remaining hypo-coordinated.

We note that the metal–metal bonding in the M1(2e–)M2 centers (where M1 and M2 are either Al or Ca) is considerably weaker than that in the M1(O2–)M2 lattice, forming weak links that disrupt polymeric Al-O structures and increase local mobility in the system, analogous to fluoride or hydroxide anions in conventional glasses. However, in addition to being far weaker than metal–oxygen bonds, electron anions are far more mobile than conventional anions and can be easily displaced. O2– ions diffusing through the lattice react with the M1(2e–)M2 centers and displace the trapped electrons either to the remnants of the C12A7 lattice cages or to other undercoordinated metal sites. Because the electron transfer occurs at a much faster timescale than atomic displacements, such electron transfer and (re)trapping events change the local potential energy surface, i.e., induce forces that accelerate atoms in the vicinity of the defects. Thus, we propose that electron anion transfer events in C12A7:e– elevate the local temperature above the global average, thus maintaining the molten phase to lower global temperatures than in a-C12A7:O2–.

Amorphous C12A7:e– and C12A7:O2– have virtually indistinguishable X-ray scattering, neutron diffraction, and infrared spectra. However, the Raman spectra of C12A7:e– show a narrow resonantly enhanced band peaking at ∼186 cm−1 and strongly increasing in intensity as a function of Ne (29). These data provide us with a reference point for the experimental validation of the proposed electronic defects and mechanisms. To test whether the Raman band is associated with electron anions, we represent the Al(2e–)Al and Al(2e–)Ca defects using linear clusters OAl–AlO (Fig. 4A) and FCa–AlO (Fig. 4B), respectively, denoted for brevity as LM–ML, where M are metals (M = Al, Ca) and L are ligands (L = O, F). These clusters reproduce critical elements of the electron defects in C12A7:e–: electrostatic neutrality, coordination of the metal atoms by ligands L, and localization of two electrons between the metal atoms similar to that in Al(2e–)Al and Al(2e–)Ca. Importantly, these models allow us to isolate the motion of the metal atoms from that of the rest of the system and calculate resonant Raman intensities as functions of M–M distances. Both LM–ML clusters exhibit a strong Raman peak due to in-phase stretching of the M–M bond. As the M–M distance increases, the intensities of the peaks increase and their frequencies decrease. The Raman spectra in Fig. 4 show that for the M–M distances close to those in the Al(2e–)Al and Al(2e–)Ca centers, the frequencies of both stretching modes are consistent with the observed 186-cm−1 peak and the resonant enhancement in LAl–CaL is approximately an order of magnitude higher than that in LAl–AlL. We note that because the excited states in the clusters are at higher energies than in the bulk C12A7:e– system, enhancement in the LAl–AlL cluster is underestimated.

(A and B) Simulated Raman spectra for simplified models of M1(2e–)M2 centers, O-Al-Al-O (A) and F-Ca-Al-O (B) under 457-nm excitation. The frequency and intensity of the Raman response are strongly dependent on the metal–metal distance. The resonant (solid triangles) and nonresonant (open squares) responses are detailed in Insets. (C) Comparison of experimental and simulated UV/visible absorption in C12A7. The Al(2e−)Ca and Al(2e−)Al centers contribute to the peaks in the imaginary dielectric function (absorption) of C12A7:e− (solid line) at 3.3 eV and 4 eV, respectively, consistent with the experimental UV/visible spectrum of C12A7:e− (right axis). The two low-energy peaks are absent in the dielectric function of the stoichiometric system (dashed line).

The computed imaginary part of the bulk dielectric function Im(ε) for a-C12A7:e– (Tmax = 2,650 K) is compared with the experimentally measured optical absorption spectrum in Fig. 4C. The two intense peaks at 3.2 eV and 4.0 eV are assigned to the transition between the bonding and antibonding orbitals of the Al(2e–)Ca and Al(2e–)Al centers, respectively, whereas the 2.5-eV peak is attributed to the electron transfer from these defects to the gap states associated with the remaining distorted lattice cages. The calculated values are in good agreement with the experimentally observed bands peaking at 3.3 eV and 4.6 eV and a low-energy tail and consistent with the optical absorption of electron anions in crystalline C12A7:e– (30), which provides further validation of the proposed electron defect models. Finally we note that the Im(ε) for a-C12A7:O2– shows no optical absorption features up to ∼5 eV in complete agreement with the experimental data (29).

Properties of glasses are modified by weakening their continuous polymeric networks with (Fig. 5) dopants that provide ionic nondirectional bonds (e.g., Na+, Ca2+) or break and terminate polymeric chains (e.g., F–). Electron anions provide a method to introduce weak links into a glass network, complementing conventional substitution of anions or cations. Furthermore, electron anions are capable of inducing such modifications at lower concentrations than conventional glass modifiers due to their exceptional mobility.

Continuous random networks of strongly bonded structural elements are modified by introducing weak links (network modifiers), including cations, such as Na+ and Ca2+, that induce the formation of ionic bonds (dashed lines) or monovalent anions, such as F− and OH−, that terminate polymerization of network fragments. Electron anions introduce another category of network modifiers: highly mobile weak links.

The strong dependence of the Tg on the concentration of electron anions in C12A7 opens up the possibility of fine-tuning the glass formation and processing approaches with small composition changes as long as the origin of this dependence is understood and the underlying mechanisms are controlled. The microscopic model presented here reveals the mechanisms of C12A7 transformation from the crystalline to the amorphous form and explains the dependence of Tg on the concentration of electron anions; it also gives insight into the multiple kinetically controlled processes near Tm. We propose that use of electrons as highly mobile anions offers a promising method for attenuating the thermal and electronic properties of amorphous materials formed from oxides of nonreducible metals, facilitating the design of structural and functional glasses and building on the recent discoveries of other stable solid electrides (44⇓⇓–47). Furthermore, the concept of altering network properties via highly mobile weak links, such as electron anions, as opposed to stationary weak links, may have applications in a diverse variety of networks, well beyond the science of noncrystalline materials.

Simulation Details

All MD and properties calculations on crystalline and amorphous C12A7 were performed using the VASP (32). Simulations of C12A7 electride were conducted in spin-polarized mode, whereas stoichiometric C12A7 was modeled in non-spin–polarized mode. Molecular dynamics trajectories were calculated using a single k-point (Γ) and default precision for the Fast Fourier Transform (FFT) grid. A 400-eV plane-wave cutoff, an energy convergence criterion of 10−5 eV, and a time step of 0.5 fs were used throughout the MD simulations. The plane-wave energy cutoff was increased to 550 eV, the reciprocal space representation expanded to a 4 × 4 × 4 Γ-centered grid, which was previously found to be adequately converged (16), and the energy convergence criterion tightened to 10−6 eV for the post-MD relaxation step. Hybrid calculations used the default screening parameter of 0.2 Bohr−1, the sum-over-states method, and a total of 640 bands. Exact exchange was evaluated using a reduced FFT grid for reasons of computational efficiency.

The topology of the crystalline and amorphous structures, distribution of rings, coordination numbers, and pairwise radial distributions were generated using the R.I.N.G.S. code 1.2.5 (39). Rings were defined by the King criterion and constrained to be irreducible (cannot be subdivided into smaller rings). Structural preprocessing (format conversion, center of mass motion correction, wrapping and unwrapping of periodic boundary conditions) and other structural analyses such as velocity distributions, velocity autocorrelation function (VACF), rmsd, and charge localization were analyzed using a series of in-house MATLAB scripts. Structural parameters (e.g., distances) and one-electron energies were low-pass filtered using second-order Savitzky–Golay averaging with a time window of 0.5 ps to remove high-frequency vibrational noise.

Partial charges were calculated using the Bader method (40). Electron anions were located by searching for large changes in the Bader charges of adjacent cations and confirmed by examining the electron density of the relevant states. Specific to our system, the Bader charge of Al species coordinated with O2– ions only is exactly 3.0 |e|. However, in the case of electron anions located between cations, described as Al(2e–)Al and Al(2e–)Ca defects, the density of the two electrons is partially assigned to the Al species, making their charge of ∼2.2 |e|. We use this feature of the Bader analysis to monitor the formation, disappearance, and diffusion of localized electronic centers.

Raman spectra were calculated for model Al(2e–)Al and Al(2e–)Ca defects represented by linear pseudomolecules. The charge distribution in Al(2e–)Al resembles that in the linear molecule O-Al-Al-O: O2–Al3+(2e–)Al3+O2– in formal charge notations. Similarly, the charge distribution in Al(2e–)Ca resembles that in F-Ca-Al-O, i.e., F–Ca2+(2e–)Al3+O2 (Fig. 4 in the main text). The O and F ligands of the metal atoms were selected such that the species was neutral and two electrons were available for metal–metal bonding. The metal–metal distance was controlled, whereas the ligand–metal distances were optimized to minimize the total energy of the molecule. These calculations were carried out using the NWChem 6.5 code (41) at the B3LYP/6-311+G(d) level of theory. Raman spectra calculations were performed for the excitation wavelengths of 308 nm, 457 nm, 532 nm, and 633 nm. Total energy was converged to 10−9 Hartree and the geometry was minimized to a rms gradient of 3 × 10−4 Hartree/Bohr.

Analysis of Melting and Quenching

Simulations of glass formation in C12A7 were conducted in three phases: (i) heating via addition of a single pulse of kinetic energy at the first time, followed by 4.0 ps of equilibration; (ii) incrementally reducing the cell volume until it corresponded to the experimental density of the glass; and (iii) quenching by removing 5.0 eV of kinetic energy every 2.0 ps. One-electron energy levels for the electron anions and the type of feature they are localized within, along with the valence band maximum (VBM) and conduction band minimum (CBM), are shown for two initial temperatures in Fig. S2.

At the lower initial temperature (1,910 K), little fluctuation is observed in the one-electron energies except for the formation of a single Al(2e−)Al center during compression, whereas large fluctuations in the one-electron energies are observed at the higher initial temperature (2,650 K) until midway through the quenching process. The drastic difference necessitates a more detailed structural examination of the material during and after quenching to verify that melting and formation of an amorphous phase have occurred.

The standard Lindemann criterion for the solid-to-melt transition has limited applicability in this case because the cages in crystalline C12A7 are flexible along their S4 symmetry axes (31); hence, large vibrational amplitudes do not necessarily indicate melting. Instead, evolution of the C12A7 structure with temperature was monitored by means of the radial distribution function for aluminum atoms gAl-Al(r), which has a well-defined structure up to the fourth coordination shell.

Because aluminum was observed to be the least mobile species in the material, loss of distinct crystalline order for aluminum atoms would manifest collapse of the Al-O-Al network, indicative of melting of the material. The Al-O radial distribution function gAl–O(r) was examined as an additional solid–melt transition metric. However, it turned out to be less convenient than gAl–Al(r) because of significant thermal broadening beyond the first coordination shell. We used localization of excess-electron charge and changes in the internal pressure of the system as additional metrics for assessing structural changes upon heating and quenching.

Structural changes in C12A7:e– during the initial 4-ps equilibration phase, represented by gAl–Al(r), are shown in Fig. S3 for several values of Tmax (the range of Tmax is defined in the main text). The radial distribution function gAl–Al(r) undergoes thermal broadening as Tmax increases, but the Al-O-Al network collapse was not observed within the first 4-ps simulation time. However, upon isothermal compression the Al-O-Al network undergoes dramatic rearrangement manifested by the loss of gAl–Al(r) structure for Tmax above 2,530 K (Fig. S3A): The outer coordination shells are replaced by the smooth, oscillating decay toward uniform density characteristic of a liquid. The negative internal pressure at these temperatures (Fig. S3B) clearly indicates that the compression ought to occur upon heating. Finally, analysis of localization of excess-electron charge near lattice Al species (Fig. S3C) allows one to pinpoint two distinct temperature ranges. Below Tmax = 2,310 K, charge localization is a rare and transient event, whereas for Tmax above 2,310 K, charge localization occurs readily and is persistent. Analysis of gAl–Al(r) and internal pressure for the quenched structures is shown in Fig. S4.

These analyses revealed two types of resulting C12A7:e–. In the case of Tmax < 2,530 K, the gAl–Al(r) indicates the existence of clearly recognizable crystalline order. As the temperature decreased, the pressure in these systems increased dramatically (Fig. S4B) and, upon postquench lattice relaxation, these structures expand until their density reaches that of the crystalline C12A7:e– (Fig. 2 in the main text). In contrast, if Tmax ≥ 2,530 K, gAl–Al(r) shows no local structure beyond the first coordination shell, as expected for an amorphous material, the internal pressure decreases with decreasing T and, upon postquench lattice relaxation, the system density is close to that of the experimentally synthesized amorphous C12A7:e– (Fig. 2 in the main text).

Finally, for Tmax ≥ 2,530 K, the first peak in gAl–Al(r) developed a small shoulder near 2.7 Å due to the presence of Al-Al bonds. The local charge density distribution in these structures suggests that they are more accurately represented as Al3+(2e–)Al3+ centers (or Al(2e–)Al, for brevity) and resemble oxygen vacancies in an Al-O network.

On the basis of this analysis we put the melting temperature of C12A7:e– at 2,530 K. Similar analysis of the structural changes was conducted for the stoichiometric C12A7 (C12A7:O2–) that yields the melting temperature of 2,550 K.

Changes of the local-to-medium range structure upon amorphization are characterized using the distribution of 4-membered and 6-membered rings. The distributions for two selected structures—the nearly crystalline and amorphous C12A7:e–—are shown in Fig. S5.

There are two types of 4-membered rings in the crystalline C12A7: Ca-O-Al-O and Al-O-Al-O. In the amorphous structure concentration of the former decreases whereas concentration of the latter increases. In addition, we observe a small but statistically significant contribution of the Ca-O-Ca-O rings (marked as “new” in Fig. S5). These results suggest that amorphization is accompanied by the appearance of the Al-rich and Ca-rich regions. Similar conclusions can be drawn from the analysis of the 6-membered ring distribution, where the concentration of the Al-O-Al-O-Ca-O decreases, whereas Al-only (Al-O-Al-O-Al-O) and Ca-only (Ca-O-Ca-O-Ca-O) rings appear, again indicating partial segregation. These results suggest that amorphous C12A7 can be represented as a disordered Al-O network coordinated with Ca2+ ions.

Acknowledgments

Calculations were performed using Pacific Northwest National Laboratory (PNNL) Institutional Computing resources. This work was supported by the Accelerated Innovation Research Initiative Turning Top Science and Ideas into High-Impact Values program of the Japan Science and Technology Agency. P.V.S. was supported by the Laboratory Directed Research and Development program at PNNL, a multiprogram national laboratory operated by Battelle for the US Department of Energy under Contract DE-AC05-76RLO1830.

Footnotes

↵1To whom correspondence may be addressed. Email: peter.sushko{at}pnnl.gov or hosono{at}msl.titech.ac.jp.

Author contributions: P.V.S. and H.H. designed research; L.E.J., P.V.S., Y.T., and H.H. performed research; L.E.J. and P.V.S. analyzed data; L.E.J., P.V.S., and H.H. wrote the paper; and H.H. directed the project.

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